Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 5 2.292406
beta0_yellow 4 1.730979
beta1_yellow 3 1.492025
beta1_pelagic 5 1.340662
beta0_pelagic 3 1.290859
beta0_black 1 1.284005
beta2_pelagic 3 1.283776
beta0_pH 3 1.258828
tau_beta0_yellow 1 1.238979
parameter n badRhat_avg
mu_beta0_yellow 1 1.228185
beta1_pH 11 1.209241
beta2_yellow 4 1.205540
beta3_pH 2 1.202599
beta1_black 9 1.183926
beta2_pH 4 1.172750
beta3_pelagic 1 1.167330
beta4_pelagic 1 1.148856
Table 2. Summary of unconverged parameters by area
afognak BSAI CSEO eastside EWYKT NG northeast NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_pelagic 0 0 1 0 0 0 0 0 1 0 0 0 1 0
beta0_pH 0 0 0 0 0 0 0 0 0 0 0 1 1 1
beta0_yellow 1 0 0 0 0 0 0 1 0 0 0 0 1 1
beta1_black 1 1 1 1 1 0 1 1 1 0 1 0 0 0
beta1_pelagic 1 0 1 0 0 0 1 0 0 0 0 0 1 1
beta1_pH 0 1 0 0 0 1 0 1 1 1 0 0 1 1
beta1_yellow 0 1 0 0 0 0 0 0 0 0 0 0 1 1
beta2_pelagic 0 0 0 0 0 0 0 1 1 0 0 0 1 0
beta2_pH 0 1 0 0 0 0 0 0 0 1 0 1 0 1
beta2_yellow 1 0 0 0 0 1 0 1 0 0 0 0 0 1
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta3_pH 0 0 0 0 0 0 0 0 0 0 0 1 0 1
beta3_yellow 0 1 0 0 0 0 0 1 0 0 0 1 1 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 1 0
mu_beta0_yellow 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.129 0.071 -0.262 -0.131 0.021
mu_bc_H[2] -0.097 0.044 -0.172 -0.100 0.005
mu_bc_H[3] -0.435 0.071 -0.571 -0.438 -0.290
mu_bc_H[4] -0.991 0.188 -1.383 -0.982 -0.634
mu_bc_H[5] 0.961 0.938 -0.165 0.783 3.443
mu_bc_H[6] -2.141 0.323 -2.754 -2.153 -1.512
mu_bc_H[7] -0.469 0.112 -0.698 -0.462 -0.259
mu_bc_H[8] 0.248 0.381 -0.351 0.205 1.095
mu_bc_H[9] -0.287 0.135 -0.566 -0.289 -0.019
mu_bc_H[10] -0.111 0.067 -0.236 -0.112 0.031
mu_bc_H[11] -0.125 0.037 -0.199 -0.125 -0.053
mu_bc_H[12] -0.251 0.107 -0.474 -0.244 -0.052
mu_bc_H[13] -0.132 0.078 -0.288 -0.132 0.028
mu_bc_H[14] -0.300 0.096 -0.499 -0.298 -0.115
mu_bc_H[15] -0.334 0.050 -0.432 -0.336 -0.233
mu_bc_H[16] -0.244 0.365 -0.863 -0.271 0.575
mu_bc_R[1] 1.298 0.144 1.026 1.297 1.594
mu_bc_R[2] 1.450 0.096 1.256 1.452 1.634
mu_bc_R[3] 1.377 0.135 1.116 1.380 1.644
mu_bc_R[4] 0.933 0.199 0.533 0.939 1.308
mu_bc_R[5] 1.137 0.476 0.198 1.146 2.065
mu_bc_R[6] -1.593 0.435 -2.434 -1.586 -0.779
mu_bc_R[7] 0.293 0.201 -0.090 0.296 0.677
mu_bc_R[8] 0.556 0.202 0.142 0.562 0.935
mu_bc_R[9] 0.333 0.207 -0.104 0.346 0.696
mu_bc_R[10] 1.326 0.125 1.063 1.332 1.554
mu_bc_R[11] 1.026 0.088 0.858 1.026 1.203
mu_bc_R[12] 0.822 0.208 0.416 0.817 1.244
mu_bc_R[13] 0.975 0.104 0.765 0.977 1.169
mu_bc_R[14] 0.930 0.147 0.626 0.932 1.210
mu_bc_R[15] 0.747 0.106 0.535 0.748 0.960
mu_bc_R[16] 1.081 0.135 0.804 1.080 1.346
tau_pH[1] 5.221 0.441 4.369 5.211 6.107
tau_pH[2] 2.779 0.332 2.172 2.764 3.478
tau_pH[3] 2.609 0.378 1.944 2.591 3.402
tau_pH[4] 8.363 1.324 6.011 8.290 11.131
beta0_pH[1,1] 0.518 0.172 0.169 0.525 0.836
beta0_pH[2,1] 1.337 0.170 0.997 1.343 1.655
beta0_pH[3,1] 1.417 0.192 0.992 1.433 1.754
beta0_pH[4,1] 1.577 0.211 1.121 1.590 1.953
beta0_pH[5,1] -0.849 0.302 -1.515 -0.823 -0.325
beta0_pH[6,1] -0.684 0.494 -2.013 -0.593 0.003
beta0_pH[7,1] 0.232 0.672 -1.225 0.608 0.959
beta0_pH[8,1] -0.698 0.310 -1.446 -0.655 -0.204
beta0_pH[9,1] -0.627 0.290 -1.252 -0.606 -0.132
beta0_pH[10,1] 0.220 0.183 -0.148 0.217 0.571
beta0_pH[11,1] -0.117 0.152 -0.426 -0.112 0.167
beta0_pH[12,1] 0.478 0.183 0.125 0.479 0.824
beta0_pH[13,1] 0.034 0.147 -0.265 0.039 0.320
beta0_pH[14,1] -0.286 0.166 -0.622 -0.281 0.028
beta0_pH[15,1] 0.020 0.174 -0.328 0.025 0.368
beta0_pH[16,1] -0.336 0.285 -0.967 -0.307 0.141
beta0_pH[1,2] 2.537 0.249 2.054 2.552 2.969
beta0_pH[2,2] 2.608 0.348 1.851 2.709 3.092
beta0_pH[3,2] 2.359 0.262 1.801 2.374 2.826
beta0_pH[4,2] 2.458 0.347 1.793 2.462 3.011
beta0_pH[5,2] 4.434 1.403 2.517 4.186 7.927
beta0_pH[6,2] 2.814 0.294 2.249 2.820 3.331
beta0_pH[7,2] 1.884 0.223 1.391 1.909 2.230
beta0_pH[8,2] 2.788 0.228 2.314 2.810 3.120
beta0_pH[9,2] 2.733 0.624 1.490 2.740 3.692
beta0_pH[10,2] 3.673 0.227 3.213 3.690 4.039
beta0_pH[11,2] -4.981 0.308 -5.628 -4.970 -4.409
beta0_pH[12,2] -4.923 0.483 -6.018 -4.875 -4.105
beta0_pH[13,2] -4.604 0.385 -5.387 -4.594 -3.867
beta0_pH[14,2] -5.773 0.445 -6.677 -5.763 -4.949
beta0_pH[15,2] -4.118 0.300 -4.713 -4.119 -3.531
beta0_pH[16,2] -4.770 0.425 -5.675 -4.760 -3.979
beta0_pH[1,3] 0.422 0.622 -0.995 0.478 1.358
beta0_pH[2,3] 1.861 0.526 0.436 2.048 2.439
beta0_pH[3,3] 2.277 0.334 1.433 2.359 2.711
beta0_pH[4,3] 2.763 0.438 1.427 2.873 3.200
beta0_pH[5,3] 0.998 1.881 -2.037 0.768 5.334
beta0_pH[6,3] -0.754 1.176 -3.137 -0.836 1.528
beta0_pH[7,3] -2.377 0.753 -4.202 -2.284 -1.179
beta0_pH[8,3] 0.240 0.192 -0.153 0.245 0.604
beta0_pH[9,3] -1.248 0.843 -3.060 -1.018 -0.136
beta0_pH[10,3] -0.655 1.060 -2.695 -0.681 0.982
beta0_pH[11,4] 0.053 0.795 -1.672 0.100 1.503
beta0_pH[12,4] -0.501 0.794 -2.156 -0.386 0.802
beta0_pH[13,4] 0.391 0.207 -0.078 0.409 0.753
beta0_pH[14,4] 1.131 0.459 -0.081 1.206 1.817
beta0_pH[15,4] 0.262 0.498 -0.190 0.212 0.731
beta0_pH[16,4] 0.600 0.504 -0.675 0.678 1.332
beta0_pH[11,5] -0.845 0.179 -1.200 -0.841 -0.500
beta0_pH[12,5] -2.249 0.488 -2.796 -2.329 -1.153
beta0_pH[13,5] -0.240 0.157 -0.561 -0.239 0.066
beta0_pH[14,5] -1.302 0.140 -1.577 -1.299 -1.038
beta0_pH[15,5] -1.184 0.150 -1.483 -1.182 -0.897
beta0_pH[16,5] -0.765 0.146 -1.062 -0.767 -0.474
beta1_pH[1,1] 3.104 0.314 2.552 3.086 3.801
beta1_pH[2,1] 2.194 0.258 1.711 2.181 2.745
beta1_pH[3,1] 2.022 0.292 1.512 1.996 2.689
beta1_pH[4,1] 2.377 0.340 1.831 2.337 3.170
beta1_pH[5,1] 2.273 0.365 1.674 2.236 3.086
beta1_pH[6,1] 3.937 1.196 2.298 3.704 6.827
beta1_pH[7,1] 2.465 1.749 0.268 2.214 7.573
beta1_pH[8,1] 4.237 1.178 2.616 3.987 7.137
beta1_pH[9,1] 2.292 0.373 1.657 2.263 3.120
beta1_pH[10,1] 2.408 0.263 1.906 2.401 2.955
beta1_pH[11,1] 3.296 0.197 2.918 3.287 3.699
beta1_pH[12,1] 2.567 0.214 2.145 2.565 2.981
beta1_pH[13,1] 2.936 0.203 2.549 2.933 3.353
beta1_pH[14,1] 3.390 0.219 2.965 3.387 3.836
beta1_pH[15,1] 2.487 0.224 2.055 2.481 2.942
beta1_pH[16,1] 3.954 0.538 3.096 3.883 5.154
beta1_pH[1,2] 1.422 2.294 0.013 0.990 7.156
beta1_pH[2,2] 2.365 6.646 0.006 0.864 17.746
beta1_pH[3,2] 1.224 0.302 0.668 1.209 1.852
beta1_pH[4,2] 4.901 31.557 0.154 0.982 23.843
beta1_pH[5,2] 1.348 3.682 0.000 0.449 7.482
beta1_pH[6,2] 1.205 1.326 0.000 1.155 3.262
beta1_pH[7,2] 0.787 1.553 0.000 0.275 4.613
beta1_pH[8,2] 0.681 1.170 0.000 0.241 4.199
beta1_pH[9,2] 1.004 1.203 0.000 1.012 2.536
beta1_pH[10,2] 4.826 7.575 0.000 2.226 27.417
beta1_pH[11,2] 6.853 0.344 6.192 6.841 7.557
beta1_pH[12,2] 6.751 0.625 5.752 6.685 8.235
beta1_pH[13,2] 7.066 0.417 6.301 7.046 7.892
beta1_pH[14,2] 7.653 0.472 6.776 7.639 8.605
beta1_pH[15,2] 6.648 0.318 6.047 6.645 7.274
beta1_pH[16,2] 7.489 0.448 6.632 7.482 8.420
beta1_pH[1,3] 3.229 1.272 1.622 2.960 6.436
beta1_pH[2,3] 1.131 2.146 0.001 0.542 6.556
beta1_pH[3,3] 1.598 10.818 0.000 0.318 8.855
beta1_pH[4,3] 1.625 3.779 0.000 0.327 14.552
beta1_pH[5,3] 4.360 3.835 1.613 3.496 13.479
beta1_pH[6,3] 2.831 1.288 1.058 2.663 5.412
beta1_pH[7,3] 3.238 0.763 2.036 3.137 5.078
beta1_pH[8,3] 2.870 0.387 2.183 2.854 3.640
beta1_pH[9,3] 3.314 0.859 2.104 3.115 5.236
beta1_pH[10,3] 4.083 1.136 2.337 4.058 6.383
beta1_pH[11,4] 2.598 0.767 1.183 2.531 4.439
beta1_pH[12,4] 3.409 0.800 2.100 3.297 5.067
beta1_pH[13,4] 2.507 0.577 1.748 2.402 3.995
beta1_pH[14,4] 2.603 1.382 1.114 2.252 6.249
beta1_pH[15,4] 2.820 0.878 1.839 2.621 5.022
beta1_pH[16,4] 2.891 1.153 1.431 2.642 5.847
beta1_pH[11,5] 2.497 0.777 1.538 2.356 4.404
beta1_pH[12,5] 4.770 3.144 2.418 4.061 11.218
beta1_pH[13,5] 3.723 2.208 2.084 3.181 9.602
beta1_pH[14,5] 2.037 1.442 1.143 1.804 4.094
beta1_pH[15,5] 2.702 0.988 1.502 2.511 5.301
beta1_pH[16,5] 3.301 1.677 1.511 2.926 7.694
beta2_pH[1,1] 0.477 0.120 0.295 0.461 0.752
beta2_pH[2,1] 0.557 0.266 0.253 0.507 1.157
beta2_pH[3,1] 0.623 0.384 0.231 0.533 1.575
beta2_pH[4,1] 0.481 0.212 0.213 0.447 0.941
beta2_pH[5,1] 1.514 1.209 0.241 1.242 4.647
beta2_pH[6,1] 0.186 0.069 0.087 0.174 0.348
beta2_pH[7,1] -0.613 1.687 -4.916 0.017 1.451
beta2_pH[8,1] 0.236 0.093 0.113 0.220 0.452
beta2_pH[9,1] 0.455 0.297 0.185 0.400 0.968
beta2_pH[10,1] 0.635 0.318 0.301 0.565 1.371
beta2_pH[11,1] 0.788 0.219 0.479 0.757 1.296
beta2_pH[12,1] 1.374 0.480 0.757 1.277 2.405
beta2_pH[13,1] 0.757 0.223 0.432 0.719 1.272
beta2_pH[14,1] 0.850 0.211 0.537 0.818 1.342
beta2_pH[15,1] 0.854 0.312 0.440 0.801 1.624
beta2_pH[16,1] 0.396 0.184 0.190 0.341 0.898
beta2_pH[1,2] -0.151 4.076 -8.809 0.686 7.321
beta2_pH[2,2] -1.500 4.154 -10.195 -1.539 6.630
beta2_pH[3,2] -3.626 2.537 -10.220 -3.001 -0.648
beta2_pH[4,2] -3.580 2.811 -10.652 -3.028 -0.133
beta2_pH[5,2] -2.488 3.931 -9.974 -2.676 6.169
beta2_pH[6,2] -3.197 3.454 -10.189 -3.099 4.666
beta2_pH[7,2] -2.995 3.713 -10.072 -3.079 5.698
beta2_pH[8,2] -2.707 3.863 -9.780 -2.879 5.935
beta2_pH[9,2] -3.214 3.571 -10.153 -3.198 5.076
beta2_pH[10,2] -3.711 3.671 -10.740 -3.674 5.290
beta2_pH[11,2] -6.758 2.515 -13.273 -6.261 -3.286
beta2_pH[12,2] -3.410 2.743 -10.115 -2.550 -0.578
beta2_pH[13,2] -3.771 2.282 -9.605 -3.018 -1.351
beta2_pH[14,2] -4.925 2.490 -11.146 -4.347 -1.834
beta2_pH[15,2] -6.569 2.437 -12.814 -6.090 -3.265
beta2_pH[16,2] -6.978 2.548 -13.314 -6.430 -3.497
beta2_pH[1,3] 1.293 2.010 0.126 0.395 7.744
beta2_pH[2,3] 0.606 3.635 -6.886 0.613 8.149
beta2_pH[3,3] -0.181 3.847 -7.829 -0.227 7.785
beta2_pH[4,3] -0.657 3.895 -7.710 -0.683 7.575
beta2_pH[5,3] 3.054 2.755 -0.192 2.420 9.934
beta2_pH[6,3] 3.092 2.970 -0.481 2.375 10.257
beta2_pH[7,3] 2.870 2.492 0.417 1.996 9.399
beta2_pH[8,3] 4.736 2.838 0.668 4.363 11.280
beta2_pH[9,3] 2.332 2.598 0.273 0.928 9.249
beta2_pH[10,3] 1.585 2.154 0.283 0.582 7.922
beta2_pH[11,4] -2.989 2.032 -8.403 -2.521 -0.473
beta2_pH[12,4] -2.406 1.947 -7.710 -1.719 -0.632
beta2_pH[13,4] 0.785 0.665 0.254 0.601 2.549
beta2_pH[14,4] 1.000 1.108 0.091 0.602 4.012
beta2_pH[15,4] 0.933 1.039 0.313 0.869 2.635
beta2_pH[16,4] 0.372 0.416 0.095 0.274 1.376
beta2_pH[11,5] -2.302 1.542 -6.228 -1.773 -0.675
beta2_pH[12,5] -3.201 2.071 -8.465 -2.721 -0.688
beta2_pH[13,5] -3.127 1.690 -7.524 -2.693 -1.110
beta2_pH[14,5] -4.214 2.196 -10.027 -3.708 -1.338
beta2_pH[15,5] -3.824 1.761 -8.238 -3.427 -1.521
beta2_pH[16,5] -2.789 1.928 -8.012 -2.253 -0.660
beta3_pH[1,1] 35.798 0.802 34.322 35.768 37.407
beta3_pH[2,1] 33.501 1.113 31.563 33.414 35.930
beta3_pH[3,1] 33.835 1.022 31.829 33.808 35.945
beta3_pH[4,1] 33.846 1.168 31.752 33.791 36.367
beta3_pH[5,1] 27.804 1.211 26.381 27.511 31.351
beta3_pH[6,1] 38.886 3.245 32.834 38.737 45.289
beta3_pH[7,1] 29.015 9.867 18.340 24.708 45.686
beta3_pH[8,1] 40.319 2.304 36.390 39.992 45.265
beta3_pH[9,1] 30.670 1.429 28.113 30.598 33.617
beta3_pH[10,1] 32.648 0.850 31.021 32.639 34.357
beta3_pH[11,1] 30.292 0.470 29.362 30.294 31.222
beta3_pH[12,1] 30.190 0.401 29.389 30.200 30.953
beta3_pH[13,1] 33.211 0.589 32.094 33.200 34.410
beta3_pH[14,1] 32.072 0.450 31.234 32.058 33.005
beta3_pH[15,1] 31.303 0.615 30.130 31.277 32.543
beta3_pH[16,1] 32.308 1.071 30.582 32.138 34.758
beta3_pH[1,2] 34.524 8.728 18.591 39.986 44.493
beta3_pH[2,2] 26.403 6.561 18.314 25.555 43.325
beta3_pH[3,2] 41.924 1.141 40.035 41.945 43.994
beta3_pH[4,2] 35.578 8.198 19.649 40.672 44.481
beta3_pH[5,2] 30.619 8.142 18.541 29.921 45.100
beta3_pH[6,2] 33.864 5.206 19.987 35.318 43.636
beta3_pH[7,2] 29.421 7.674 18.445 28.594 44.820
beta3_pH[8,2] 29.005 7.416 18.368 28.074 44.474
beta3_pH[9,2] 38.409 8.838 19.291 43.644 45.778
beta3_pH[10,2] 29.171 5.222 19.072 29.497 41.778
beta3_pH[11,2] 43.359 0.149 43.124 43.340 43.702
beta3_pH[12,2] 43.143 0.244 42.556 43.149 43.611
beta3_pH[13,2] 43.850 0.132 43.554 43.868 44.085
beta3_pH[14,2] 43.289 0.150 43.066 43.270 43.622
beta3_pH[15,2] 43.382 0.151 43.128 43.367 43.716
beta3_pH[16,2] 43.485 0.159 43.196 43.482 43.792
beta3_pH[1,3] 38.455 2.272 33.847 38.814 42.815
beta3_pH[2,3] 30.618 7.225 18.610 30.968 44.578
beta3_pH[3,3] 30.381 8.629 18.435 29.994 44.525
beta3_pH[4,3] 27.645 7.492 18.322 25.678 44.713
beta3_pH[5,3] 26.521 6.600 18.312 25.056 42.747
beta3_pH[6,3] 27.228 6.516 18.601 25.745 44.163
beta3_pH[7,3] 26.330 1.040 24.367 26.281 28.606
beta3_pH[8,3] 41.521 0.375 40.907 41.499 42.185
beta3_pH[9,3] 31.951 1.920 27.624 32.648 34.157
beta3_pH[10,3] 34.087 1.596 31.184 33.948 36.557
beta3_pH[11,4] 44.398 1.105 41.797 44.505 45.925
beta3_pH[12,4] 41.995 0.759 40.700 42.055 42.905
beta3_pH[13,4] 31.569 1.120 29.969 31.361 34.245
beta3_pH[14,4] 30.973 1.944 29.088 30.448 36.601
beta3_pH[15,4] 30.585 1.598 29.311 30.335 33.247
beta3_pH[16,4] 33.036 2.556 29.281 32.745 38.982
beta3_pH[11,5] 40.459 0.672 39.251 40.432 41.917
beta3_pH[12,5] 38.846 1.632 36.391 38.672 42.557
beta3_pH[13,5] 40.824 0.386 39.905 40.870 41.483
beta3_pH[14,5] 39.688 0.379 39.047 39.693 40.450
beta3_pH[15,5] 40.746 0.329 40.170 40.750 41.278
beta3_pH[16,5] 38.393 1.048 36.043 38.531 40.075
beta0_pelagic[1] 1.971 0.373 1.026 2.089 2.413
beta0_pelagic[2] 1.361 0.301 0.498 1.445 1.713
beta0_pelagic[3] 0.242 0.356 -0.678 0.299 0.811
beta0_pelagic[4] 0.354 0.320 -0.268 0.340 1.012
beta0_pelagic[5] 0.138 1.479 -3.211 0.978 1.467
beta0_pelagic[6] 1.198 0.450 -0.003 1.356 1.686
beta0_pelagic[7] 1.582 0.140 1.294 1.585 1.847
beta0_pelagic[8] 1.709 0.156 1.406 1.716 1.978
beta0_pelagic[9] 2.297 0.636 0.653 2.555 2.956
beta0_pelagic[10] 2.531 0.178 2.176 2.544 2.799
beta0_pelagic[11] -0.241 0.399 -1.254 -0.179 0.369
beta0_pelagic[12] 1.677 0.136 1.407 1.679 1.941
beta0_pelagic[13] 0.304 0.209 -0.165 0.316 0.658
beta0_pelagic[14] -0.146 0.274 -0.780 -0.130 0.334
beta0_pelagic[15] -0.253 0.131 -0.507 -0.254 0.003
beta0_pelagic[16] 0.211 0.286 -0.458 0.272 0.630
beta1_pelagic[1] 0.282 0.413 0.000 0.071 1.271
beta1_pelagic[2] 0.195 0.293 0.000 0.044 1.056
beta1_pelagic[3] 0.815 0.468 0.000 0.749 2.097
beta1_pelagic[4] 0.808 0.356 0.001 0.838 1.451
beta1_pelagic[5] 1.100 1.584 0.000 0.010 4.606
beta1_pelagic[6] 0.377 0.577 0.000 0.009 1.826
beta1_pelagic[7] 4.091 8.411 0.000 0.006 29.250
beta1_pelagic[8] 0.158 0.721 0.000 0.002 1.555
beta1_pelagic[9] 0.577 0.823 0.000 0.044 2.702
beta1_pelagic[10] 0.215 1.196 0.000 0.002 1.748
beta1_pelagic[11] 4.321 0.867 2.799 4.270 6.080
beta1_pelagic[12] 2.821 0.300 2.256 2.813 3.428
beta1_pelagic[13] 3.059 0.782 1.747 2.997 4.735
beta1_pelagic[14] 4.596 1.013 3.043 4.432 6.917
beta1_pelagic[15] 2.916 0.254 2.420 2.912 3.426
beta1_pelagic[16] 3.827 0.974 2.782 3.464 6.440
beta2_pelagic[1] 1.938 3.116 -4.783 1.770 8.445
beta2_pelagic[2] 1.899 2.828 -3.498 1.851 7.639
beta2_pelagic[3] 2.089 2.257 0.085 1.470 7.920
beta2_pelagic[4] 2.712 2.467 0.147 2.174 8.691
beta2_pelagic[5] -0.878 3.854 -8.214 -1.482 7.230
beta2_pelagic[6] 0.864 3.804 -7.289 0.871 8.528
beta2_pelagic[7] -1.169 3.620 -9.058 -1.010 6.489
beta2_pelagic[8] -0.289 3.992 -8.282 -0.310 7.977
beta2_pelagic[9] 0.723 3.682 -7.552 0.713 8.038
beta2_pelagic[10] -0.171 4.016 -8.435 -0.162 8.254
beta2_pelagic[11] 0.201 0.067 0.108 0.191 0.372
beta2_pelagic[12] 4.692 2.602 1.153 4.158 11.141
beta2_pelagic[13] 0.678 0.967 0.187 0.410 3.281
beta2_pelagic[14] 0.292 0.158 0.160 0.269 0.562
beta2_pelagic[15] 4.724 2.327 1.388 4.364 10.414
beta2_pelagic[16] 2.532 2.760 0.189 0.966 9.424
beta3_pelagic[1] 27.874 7.878 18.422 24.847 44.957
beta3_pelagic[2] 28.155 8.054 18.321 26.019 44.961
beta3_pelagic[3] 29.890 4.485 21.953 29.914 41.984
beta3_pelagic[4] 26.022 2.969 21.523 25.806 34.229
beta3_pelagic[5] 35.104 9.984 18.707 36.556 45.992
beta3_pelagic[6] 30.424 7.083 18.688 29.984 44.573
beta3_pelagic[7] 27.278 8.266 18.373 24.527 44.747
beta3_pelagic[8] 29.395 8.133 18.382 27.826 45.211
beta3_pelagic[9] 29.644 6.821 18.777 28.373 44.087
beta3_pelagic[10] 29.281 8.227 18.350 27.816 44.993
beta3_pelagic[11] 41.769 2.351 36.235 41.966 45.574
beta3_pelagic[12] 43.456 0.255 43.009 43.445 43.942
beta3_pelagic[13] 43.021 1.390 40.316 43.012 45.616
beta3_pelagic[14] 42.635 1.730 38.742 42.667 45.682
beta3_pelagic[15] 43.168 0.213 42.686 43.173 43.567
beta3_pelagic[16] 42.967 0.994 40.593 43.163 44.939
mu_beta0_pelagic[1] 0.920 0.839 -0.844 0.932 2.640
mu_beta0_pelagic[2] 1.535 0.692 -0.156 1.657 2.655
mu_beta0_pelagic[3] 0.261 0.468 -0.665 0.267 1.220
tau_beta0_pelagic[1] 1.240 2.211 0.063 0.692 5.651
tau_beta0_pelagic[2] 1.629 2.151 0.079 1.022 6.374
tau_beta0_pelagic[3] 1.426 1.101 0.169 1.147 4.196
beta0_yellow[1] -0.545 0.184 -0.973 -0.525 -0.250
beta0_yellow[2] 0.476 0.159 0.143 0.484 0.766
beta0_yellow[3] -0.312 0.184 -0.673 -0.307 0.027
beta0_yellow[4] 0.746 0.327 -0.152 0.823 1.163
beta0_yellow[5] -1.200 0.415 -2.041 -1.187 -0.396
beta0_yellow[6] 0.277 0.209 -0.131 0.279 0.687
beta0_yellow[7] 0.697 0.732 -1.242 0.993 1.325
beta0_yellow[8] 0.725 0.601 -0.972 0.938 1.291
beta0_yellow[9] -0.105 0.296 -0.623 -0.105 0.472
beta0_yellow[10] 0.231 0.149 -0.065 0.230 0.532
beta0_yellow[11] -1.929 0.441 -2.909 -1.928 -1.114
beta0_yellow[12] -3.634 0.437 -4.570 -3.614 -2.835
beta0_yellow[13] -3.832 0.468 -4.810 -3.819 -2.970
beta0_yellow[14] -1.984 0.657 -3.049 -2.076 -0.257
beta0_yellow[15] -2.831 0.471 -3.808 -2.814 -1.949
beta0_yellow[16] -1.768 1.059 -3.266 -2.167 -0.187
beta1_yellow[1] 0.474 0.672 0.000 0.278 2.020
beta1_yellow[2] 1.129 0.418 0.614 1.070 2.260
beta1_yellow[3] 0.673 0.306 0.062 0.665 1.280
beta1_yellow[4] 1.627 0.931 0.679 1.302 4.323
beta1_yellow[5] 4.659 11.114 1.296 2.833 29.770
beta1_yellow[6] 2.253 0.345 1.600 2.238 2.941
beta1_yellow[7] 6.037 7.676 0.332 3.510 31.286
beta1_yellow[8] 2.254 2.576 0.017 1.749 9.004
beta1_yellow[9] 1.595 0.536 0.838 1.556 2.462
beta1_yellow[10] 2.313 0.458 1.514 2.288 3.272
beta1_yellow[11] 2.096 0.444 1.233 2.099 3.025
beta1_yellow[12] 2.449 0.458 1.586 2.430 3.439
beta1_yellow[13] 2.981 0.471 2.122 2.962 3.953
beta1_yellow[14] 2.133 0.648 0.709 2.174 3.334
beta1_yellow[15] 2.123 0.473 1.229 2.113 3.085
beta1_yellow[16] 1.860 0.851 0.169 2.068 3.110
beta2_yellow[1] -1.997 2.542 -8.209 -1.490 2.162
beta2_yellow[2] -1.888 1.784 -6.659 -1.302 -0.175
beta2_yellow[3] -2.270 2.077 -7.604 -1.612 -0.128
beta2_yellow[4] -1.781 2.176 -7.696 -0.849 -0.081
beta2_yellow[5] -4.194 2.766 -10.679 -3.648 -0.467
beta2_yellow[6] 3.609 2.264 0.919 3.014 9.393
beta2_yellow[7] -2.879 4.358 -11.004 -3.270 6.877
beta2_yellow[8] -1.622 3.527 -8.817 -1.765 6.782
beta2_yellow[9] 3.810 2.587 0.223 3.446 9.378
beta2_yellow[10] -4.537 2.833 -11.543 -3.985 -0.767
beta2_yellow[11] -3.809 2.066 -9.039 -3.382 -1.203
beta2_yellow[12] -3.893 2.053 -9.027 -3.492 -1.102
beta2_yellow[13] -3.936 1.894 -8.679 -3.572 -1.466
beta2_yellow[14] -3.558 2.214 -8.915 -3.521 -0.075
beta2_yellow[15] -3.451 2.140 -8.751 -3.121 -0.597
beta2_yellow[16] -3.738 2.246 -9.083 -3.456 -0.094
beta3_yellow[1] 27.761 7.826 18.342 25.351 44.619
beta3_yellow[2] 29.140 2.076 23.686 29.060 32.962
beta3_yellow[3] 32.960 3.188 24.651 32.964 39.732
beta3_yellow[4] 28.998 4.035 20.198 28.255 36.500
beta3_yellow[5] 33.142 1.954 27.748 33.363 35.339
beta3_yellow[6] 39.679 0.542 38.732 39.633 40.943
beta3_yellow[7] 21.654 3.920 18.618 20.221 32.784
beta3_yellow[8] 25.328 5.992 18.302 24.180 43.274
beta3_yellow[9] 37.623 2.355 35.881 37.573 42.755
beta3_yellow[10] 29.323 0.635 27.711 29.413 30.163
beta3_yellow[11] 45.299 0.509 44.109 45.390 45.971
beta3_yellow[12] 43.394 0.454 42.573 43.350 44.377
beta3_yellow[13] 44.892 0.341 44.106 44.946 45.461
beta3_yellow[14] 43.357 3.218 31.576 44.200 45.783
beta3_yellow[15] 44.839 2.386 43.740 45.165 45.961
beta3_yellow[16] 39.871 6.314 29.967 44.069 45.728
mu_beta0_yellow[1] 0.071 0.544 -1.058 0.066 1.191
mu_beta0_yellow[2] 0.093 0.491 -0.934 0.102 1.067
mu_beta0_yellow[3] -2.248 0.754 -3.421 -2.370 -0.488
tau_beta0_yellow[1] 1.974 2.211 0.103 1.258 8.395
tau_beta0_yellow[2] 1.540 2.723 0.165 1.032 5.460
tau_beta0_yellow[3] 1.130 1.732 0.069 0.624 5.044
beta0_black[1] -0.086 0.150 -0.373 -0.084 0.202
beta0_black[2] 1.828 0.221 1.332 1.861 2.116
beta0_black[3] 1.247 0.198 0.824 1.272 1.532
beta0_black[4] 1.978 0.258 1.377 2.005 2.409
beta0_black[5] 1.576 1.950 -2.807 1.653 5.247
beta0_black[6] 1.525 1.951 -3.246 1.627 5.490
beta0_black[7] 1.583 1.951 -2.880 1.653 5.601
beta0_black[8] 1.272 0.218 0.855 1.269 1.700
beta0_black[9] 2.425 0.263 1.946 2.426 2.906
beta0_black[10] 1.470 0.126 1.229 1.467 1.721
beta0_black[11] 3.385 0.244 2.792 3.414 3.740
beta0_black[12] 4.497 0.184 4.132 4.501 4.854
beta0_black[13] -0.113 0.218 -0.561 -0.108 0.307
beta0_black[14] 2.150 0.473 0.869 2.235 2.752
beta0_black[15] 1.098 0.392 0.072 1.182 1.536
beta0_black[16] 3.666 1.134 0.144 4.150 4.539
beta2_black[1] 3.448 2.320 0.746 2.827 9.383
beta2_black[2] -0.482 4.134 -8.729 -0.696 8.593
beta2_black[3] 0.471 4.033 -7.638 0.517 8.659
beta2_black[4] -2.424 2.658 -9.017 -1.672 -0.061
beta2_black[5] -0.109 4.287 -8.764 -0.100 8.447
beta2_black[6] -0.064 4.344 -8.640 -0.119 8.598
beta2_black[7] -0.139 4.364 -8.925 -0.088 8.834
beta2_black[8] -0.101 4.363 -8.550 -0.209 9.116
beta2_black[9] 0.012 4.311 -8.550 -0.004 8.432
beta2_black[10] -0.170 4.241 -8.446 -0.235 8.449
beta2_black[11] -2.311 2.592 -8.269 -1.875 2.642
beta2_black[12] -3.280 2.054 -8.546 -2.904 -0.675
beta2_black[13] -2.560 2.033 -8.130 -1.887 -0.535
beta2_black[14] -2.033 2.098 -7.308 -1.245 -0.106
beta2_black[15] -2.281 2.637 -8.481 -1.824 2.445
beta2_black[16] -1.284 2.990 -7.761 -1.077 4.579
beta3_black[1] 41.711 1.313 40.023 41.882 42.959
beta3_black[2] 29.810 8.187 18.369 29.316 44.869
beta3_black[3] 29.372 7.868 18.389 29.247 44.932
beta3_black[4] 32.921 3.541 22.498 32.825 39.407
beta3_black[5] 30.257 7.960 18.504 29.396 45.062
beta3_black[6] 30.098 7.939 18.506 29.299 45.039
beta3_black[7] 29.908 7.785 18.457 29.068 44.747
beta3_black[8] 29.925 7.803 18.471 28.759 44.718
beta3_black[9] 29.778 7.907 18.470 28.993 44.906
beta3_black[10] 30.244 8.018 18.502 29.390 45.123
beta3_black[11] 29.643 6.830 18.573 29.519 43.792
beta3_black[12] 32.939 0.868 31.092 33.046 33.919
beta3_black[13] 39.331 0.709 37.772 39.399 40.432
beta3_black[14] 38.231 3.600 28.597 38.804 44.853
beta3_black[15] 31.767 7.978 18.669 31.684 45.106
beta3_black[16] 28.275 7.207 18.344 27.146 44.509
beta4_black[1] -0.255 0.185 -0.622 -0.253 0.111
beta4_black[2] 0.249 0.171 -0.095 0.247 0.586
beta4_black[3] -0.936 0.183 -1.287 -0.934 -0.589
beta4_black[4] 0.561 0.222 0.134 0.558 0.995
beta4_black[5] 0.252 2.319 -4.053 0.159 5.062
beta4_black[6] 0.253 2.352 -4.507 0.187 4.649
beta4_black[7] 0.216 2.251 -4.142 0.123 4.937
beta4_black[8] -0.698 0.360 -1.402 -0.699 0.032
beta4_black[9] 1.473 1.008 -0.135 1.355 3.813
beta4_black[10] 0.027 0.176 -0.313 0.028 0.374
beta4_black[11] -0.691 0.208 -1.092 -0.692 -0.276
beta4_black[12] 0.297 0.326 -0.329 0.286 0.968
beta4_black[13] -1.187 0.211 -1.620 -1.186 -0.781
beta4_black[14] -0.121 0.230 -0.570 -0.124 0.326
beta4_black[15] -0.890 0.206 -1.296 -0.889 -0.487
beta4_black[16] -0.605 0.218 -1.033 -0.601 -0.174
mu_beta0_black[1] 1.160 0.853 -0.720 1.183 2.845
mu_beta0_black[2] 1.574 0.871 -0.539 1.630 3.219
mu_beta0_black[3] 2.246 0.987 0.160 2.265 4.099
tau_beta0_black[1] 0.816 0.815 0.060 0.552 3.044
tau_beta0_black[2] 2.099 4.451 0.058 0.880 10.728
tau_beta0_black[3] 0.258 0.177 0.052 0.215 0.728
beta0_dsr[11] -2.923 0.280 -3.475 -2.925 -2.374
beta0_dsr[12] 4.502 0.270 3.976 4.503 5.046
beta0_dsr[13] -1.366 0.271 -1.903 -1.368 -0.838
beta0_dsr[14] -3.711 0.486 -4.649 -3.720 -2.784
beta0_dsr[15] -1.965 0.271 -2.492 -1.966 -1.447
beta0_dsr[16] -3.098 0.381 -3.845 -3.094 -2.374
beta1_dsr[11] 4.868 0.292 4.305 4.870 5.430
beta1_dsr[12] 6.782 9.463 2.266 5.089 19.570
beta1_dsr[13] 2.821 0.274 2.269 2.824 3.368
beta1_dsr[14] 6.349 0.516 5.356 6.348 7.353
beta1_dsr[15] 3.311 0.274 2.766 3.309 3.848
beta1_dsr[16] 5.895 0.390 5.128 5.893 6.648
beta2_dsr[11] -9.197 3.022 -15.951 -8.535 -4.831
beta2_dsr[12] -7.419 2.835 -13.796 -7.205 -2.449
beta2_dsr[13] -7.004 2.825 -12.987 -6.822 -2.251
beta2_dsr[14] -6.321 2.869 -12.678 -6.184 -1.777
beta2_dsr[15] -8.150 2.627 -14.120 -7.807 -3.932
beta2_dsr[16] -8.269 2.541 -14.343 -7.872 -4.348
beta3_dsr[11] 43.486 0.154 43.208 43.480 43.779
beta3_dsr[12] 34.007 0.751 32.221 34.151 34.829
beta3_dsr[13] 43.250 0.253 42.896 43.184 43.830
beta3_dsr[14] 43.331 0.223 43.075 43.265 43.898
beta3_dsr[15] 43.512 0.186 43.170 43.506 43.855
beta3_dsr[16] 43.437 0.156 43.176 43.429 43.759
beta4_dsr[11] 0.583 0.210 0.175 0.581 1.020
beta4_dsr[12] 0.269 0.437 -0.574 0.272 1.154
beta4_dsr[13] -0.131 0.210 -0.568 -0.127 0.266
beta4_dsr[14] 0.174 0.240 -0.310 0.182 0.640
beta4_dsr[15] 0.768 0.209 0.355 0.770 1.173
beta4_dsr[16] 0.168 0.222 -0.281 0.168 0.600
beta0_slope[11] -1.908 0.161 -2.222 -1.909 -1.596
beta0_slope[12] -4.655 0.260 -5.164 -4.651 -4.161
beta0_slope[13] -1.467 0.280 -2.233 -1.425 -1.079
beta0_slope[14] -2.640 0.174 -2.981 -2.639 -2.311
beta0_slope[15] -1.436 0.164 -1.735 -1.439 -1.093
beta0_slope[16] -2.753 0.172 -3.096 -2.750 -2.421
beta1_slope[11] 4.583 0.296 4.005 4.583 5.167
beta1_slope[12] 5.087 0.517 4.117 5.068 6.132
beta1_slope[13] 3.104 0.746 2.282 2.913 5.398
beta1_slope[14] 6.526 0.545 5.490 6.515 7.607
beta1_slope[15] 3.085 0.281 2.537 3.081 3.631
beta1_slope[16] 5.402 0.383 4.626 5.403 6.143
beta2_slope[11] 8.019 2.354 4.381 7.664 13.670
beta2_slope[12] 7.063 2.540 2.703 6.820 12.921
beta2_slope[13] 5.068 3.156 0.255 5.167 11.406
beta2_slope[14] 6.399 2.470 2.313 6.185 11.973
beta2_slope[15] 7.472 2.370 3.645 7.184 13.210
beta2_slope[16] 7.707 2.443 3.904 7.341 13.516
beta3_slope[11] 43.477 0.150 43.198 43.478 43.760
beta3_slope[12] 43.383 0.216 43.053 43.353 43.812
beta3_slope[13] 43.590 0.538 42.704 43.629 44.814
beta3_slope[14] 43.320 0.173 43.098 43.278 43.757
beta3_slope[15] 43.512 0.190 43.154 43.510 43.871
beta3_slope[16] 43.449 0.174 43.160 43.431 43.800
beta4_slope[11] -0.597 0.214 -1.027 -0.596 -0.183
beta4_slope[12] -1.495 0.692 -3.007 -1.409 -0.402
beta4_slope[13] 0.116 0.213 -0.303 0.111 0.528
beta4_slope[14] -0.174 0.249 -0.652 -0.174 0.324
beta4_slope[15] -0.674 0.209 -1.095 -0.674 -0.275
beta4_slope[16] -0.164 0.230 -0.598 -0.170 0.287
sigma_H[1] 0.198 0.053 0.098 0.195 0.306
sigma_H[2] 0.171 0.030 0.119 0.169 0.236
sigma_H[3] 0.196 0.043 0.119 0.193 0.287
sigma_H[4] 0.417 0.077 0.295 0.409 0.592
sigma_H[5] 0.996 0.207 0.612 0.983 1.435
sigma_H[6] 0.394 0.206 0.029 0.388 0.816
sigma_H[7] 0.295 0.057 0.203 0.289 0.420
sigma_H[8] 0.415 0.087 0.281 0.405 0.604
sigma_H[9] 0.527 0.128 0.331 0.511 0.821
sigma_H[10] 0.215 0.043 0.141 0.211 0.311
sigma_H[11] 0.279 0.046 0.203 0.274 0.378
sigma_H[12] 0.436 0.166 0.210 0.406 0.776
sigma_H[13] 0.218 0.038 0.152 0.216 0.295
sigma_H[14] 0.520 0.097 0.353 0.512 0.724
sigma_H[15] 0.247 0.041 0.177 0.243 0.341
sigma_H[16] 0.224 0.043 0.151 0.220 0.319
lambda_H[1] 3.143 4.170 0.164 1.779 14.172
lambda_H[2] 8.249 7.537 0.795 6.048 29.241
lambda_H[3] 6.256 10.302 0.256 2.992 33.104
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.982 8.238 0.034 1.101 29.568
lambda_H[6] 8.176 16.014 0.009 1.262 54.405
lambda_H[7] 0.014 0.010 0.002 0.011 0.040
lambda_H[8] 8.644 10.806 0.132 5.075 39.129
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.361 1.645 0.033 0.207 1.321
lambda_H[11] 0.268 0.386 0.012 0.133 1.271
lambda_H[12] 4.897 6.489 0.173 2.853 22.131
lambda_H[13] 3.476 3.380 0.242 2.521 12.302
lambda_H[14] 3.273 3.780 0.197 2.020 14.189
lambda_H[15] 0.026 0.064 0.003 0.016 0.095
lambda_H[16] 0.698 0.968 0.043 0.359 3.426
mu_lambda_H[1] 4.387 1.923 1.311 4.175 8.604
mu_lambda_H[2] 3.896 1.933 0.755 3.739 8.023
mu_lambda_H[3] 3.510 1.834 0.773 3.246 7.625
sigma_lambda_H[1] 8.650 4.304 2.197 7.906 18.410
sigma_lambda_H[2] 8.443 4.610 1.281 7.947 18.305
sigma_lambda_H[3] 6.330 3.991 1.029 5.458 15.998
beta_H[1,1] 6.891 1.071 4.338 7.047 8.531
beta_H[2,1] 9.883 0.481 8.832 9.908 10.783
beta_H[3,1] 7.974 0.788 6.184 8.061 9.284
beta_H[4,1] 9.307 7.927 -7.094 9.445 24.727
beta_H[5,1] 0.180 2.227 -4.295 0.351 4.147
beta_H[6,1] 3.267 3.838 -6.790 4.615 7.576
beta_H[7,1] 0.754 5.764 -11.528 1.222 10.689
beta_H[8,1] 1.304 3.402 -2.306 1.263 3.407
beta_H[9,1] 12.887 5.813 1.725 12.831 24.591
beta_H[10,1] 7.124 1.703 3.592 7.203 10.386
beta_H[11,1] 5.191 3.499 -2.754 5.954 10.004
beta_H[12,1] 2.596 1.081 0.716 2.538 4.958
beta_H[13,1] 9.058 0.868 7.183 9.130 10.604
beta_H[14,1] 2.209 1.014 0.134 2.209 4.187
beta_H[15,1] -6.425 3.849 -13.165 -6.669 2.004
beta_H[16,1] 3.592 2.708 -0.738 3.241 9.874
beta_H[1,2] 7.908 0.240 7.418 7.920 8.341
beta_H[2,2] 10.025 0.134 9.756 10.026 10.285
beta_H[3,2] 8.956 0.201 8.558 8.952 9.367
beta_H[4,2] 3.572 1.496 0.713 3.532 6.617
beta_H[5,2] 1.946 0.946 0.054 1.972 3.743
beta_H[6,2] 5.751 1.026 3.207 5.933 7.361
beta_H[7,2] 2.550 1.116 0.588 2.496 4.922
beta_H[8,2] 3.031 0.977 1.441 3.159 4.256
beta_H[9,2] 3.556 1.127 1.469 3.495 5.830
beta_H[10,2] 8.189 0.351 7.487 8.207 8.841
beta_H[11,2] 9.753 0.636 8.818 9.624 11.243
beta_H[12,2] 3.938 0.371 3.252 3.931 4.716
beta_H[13,2] 9.130 0.255 8.678 9.120 9.652
beta_H[14,2] 4.032 0.355 3.353 4.019 4.756
beta_H[15,2] 11.420 0.699 9.930 11.449 12.678
beta_H[16,2] 4.502 0.813 2.956 4.491 6.129
beta_H[1,3] 8.467 0.240 8.032 8.453 8.965
beta_H[2,3] 10.068 0.114 9.847 10.068 10.292
beta_H[3,3] 9.619 0.157 9.319 9.614 9.948
beta_H[4,3] -2.495 0.888 -4.269 -2.479 -0.801
beta_H[5,3] 3.822 0.609 2.558 3.822 4.974
beta_H[6,3] 7.897 1.156 6.339 7.535 10.564
beta_H[7,3] -2.606 0.733 -4.028 -2.619 -1.154
beta_H[8,3] 5.231 0.463 4.638 5.180 6.126
beta_H[9,3] -2.892 0.746 -4.344 -2.865 -1.414
beta_H[10,3] 8.701 0.278 8.164 8.697 9.257
beta_H[11,3] 8.552 0.285 7.929 8.577 9.029
beta_H[12,3] 5.257 0.325 4.490 5.300 5.789
beta_H[13,3] 8.815 0.177 8.449 8.822 9.150
beta_H[14,3] 5.692 0.283 5.065 5.714 6.181
beta_H[15,3] 10.317 0.326 9.704 10.308 10.977
beta_H[16,3] 6.145 0.564 4.991 6.172 7.163
beta_H[1,4] 8.268 0.178 7.881 8.277 8.585
beta_H[2,4] 10.130 0.122 9.874 10.137 10.346
beta_H[3,4] 10.119 0.168 9.753 10.134 10.422
beta_H[4,4] 11.806 0.455 10.892 11.812 12.683
beta_H[5,4] 5.451 0.734 4.291 5.351 7.175
beta_H[6,4] 7.095 0.895 5.022 7.366 8.262
beta_H[7,4] 8.203 0.340 7.534 8.209 8.870
beta_H[8,4] 6.712 0.235 6.267 6.727 7.120
beta_H[9,4] 7.198 0.476 6.250 7.202 8.160
beta_H[10,4] 7.770 0.240 7.327 7.757 8.278
beta_H[11,4] 9.392 0.197 9.004 9.388 9.779
beta_H[12,4] 7.141 0.215 6.730 7.134 7.591
beta_H[13,4] 9.041 0.144 8.739 9.043 9.315
beta_H[14,4] 7.723 0.226 7.285 7.719 8.182
beta_H[15,4] 9.469 0.239 9.009 9.465 9.942
beta_H[16,4] 9.372 0.235 8.949 9.361 9.846
beta_H[1,5] 8.985 0.147 8.690 8.990 9.274
beta_H[2,5] 10.785 0.094 10.600 10.781 10.981
beta_H[3,5] 10.925 0.170 10.627 10.919 11.268
beta_H[4,5] 8.381 0.464 7.500 8.368 9.357
beta_H[5,5] 5.406 0.577 4.038 5.445 6.418
beta_H[6,5] 8.760 0.621 7.861 8.622 10.294
beta_H[7,5] 6.817 0.335 6.192 6.812 7.491
beta_H[8,5] 8.216 0.207 7.840 8.206 8.619
beta_H[9,5] 8.215 0.479 7.257 8.206 9.175
beta_H[10,5] 10.076 0.236 9.600 10.077 10.526
beta_H[11,5] 11.495 0.228 11.051 11.495 11.942
beta_H[12,5] 8.480 0.199 8.088 8.481 8.862
beta_H[13,5] 10.024 0.131 9.768 10.019 10.283
beta_H[14,5] 9.202 0.242 8.757 9.192 9.710
beta_H[15,5] 11.167 0.252 10.661 11.170 11.660
beta_H[16,5] 9.916 0.180 9.551 9.923 10.260
beta_H[1,6] 10.180 0.195 9.841 10.166 10.603
beta_H[2,6] 11.514 0.107 11.294 11.515 11.727
beta_H[3,6] 10.803 0.165 10.438 10.817 11.094
beta_H[4,6] 12.892 0.813 11.309 12.893 14.462
beta_H[5,6] 5.862 0.610 4.723 5.846 7.072
beta_H[6,6] 8.770 0.677 6.892 8.877 9.758
beta_H[7,6] 9.813 0.567 8.685 9.818 10.874
beta_H[8,6] 9.515 0.262 9.018 9.534 9.940
beta_H[9,6] 8.465 0.777 6.962 8.459 10.003
beta_H[10,6] 9.519 0.319 8.845 9.545 10.072
beta_H[11,6] 10.827 0.348 10.089 10.849 11.452
beta_H[12,6] 9.371 0.262 8.905 9.356 9.919
beta_H[13,6] 11.050 0.166 10.751 11.041 11.397
beta_H[14,6] 9.819 0.298 9.196 9.829 10.395
beta_H[15,6] 10.828 0.437 9.972 10.826 11.670
beta_H[16,6] 10.536 0.243 10.035 10.548 10.996
beta_H[1,7] 10.871 0.869 8.688 10.981 12.271
beta_H[2,7] 12.220 0.442 11.309 12.222 13.071
beta_H[3,7] 10.534 0.661 9.118 10.576 11.681
beta_H[4,7] 2.422 4.152 -5.400 2.469 10.652
beta_H[5,7] 6.403 1.897 3.074 6.351 10.434
beta_H[6,7] 9.631 2.422 4.834 9.513 16.071
beta_H[7,7] 10.779 2.801 5.318 10.768 16.216
beta_H[8,7] 10.948 0.954 9.462 10.907 12.654
beta_H[9,7] 4.464 3.941 -3.491 4.664 11.901
beta_H[10,7] 9.775 1.455 7.148 9.673 12.998
beta_H[11,7] 10.943 1.675 7.838 10.838 14.520
beta_H[12,7] 9.978 0.952 7.809 10.066 11.516
beta_H[13,7] 11.683 0.759 9.975 11.767 12.926
beta_H[14,7] 10.385 0.975 8.283 10.460 12.118
beta_H[15,7] 12.064 2.244 7.759 12.009 16.524
beta_H[16,7] 12.364 1.280 10.259 12.220 15.257
beta0_H[1] 8.644 12.989 -17.490 8.566 34.618
beta0_H[2] 10.691 6.213 -1.429 10.727 23.556
beta0_H[3] 9.894 10.170 -10.712 9.942 29.874
beta0_H[4] 13.169 183.086 -343.172 11.355 373.166
beta0_H[5] 4.382 22.698 -38.174 4.235 51.214
beta0_H[6] 8.335 54.313 -95.787 7.579 119.754
beta0_H[7] 5.499 133.871 -252.906 5.924 285.024
beta0_H[8] 6.990 25.430 -18.267 6.231 27.503
beta0_H[9] 3.362 122.531 -233.889 2.087 265.796
beta0_H[10] 9.449 32.214 -54.410 9.501 74.110
beta0_H[11] 10.162 47.029 -86.165 9.622 120.890
beta0_H[12] 7.004 11.425 -15.618 6.786 31.722
beta0_H[13] 9.540 10.795 -12.057 9.676 30.241
beta0_H[14] 6.882 11.925 -17.812 6.717 32.531
beta0_H[15] 10.349 106.412 -202.896 9.130 224.942
beta0_H[16] 8.048 26.462 -46.496 7.773 62.150